Calculate the energy of half a mole of photons of a radiation with a frequency of $3 \times 10^{12} \ Hz$.

What is the relation between radius, order of orbit, and nuclear charge for hydrogen-like species?

$A$ $50 \, W$ bulb emits monochromatic red light of wavelength $795 \, nm$. The number of photons emitted per second by the bulb is $x \times 10^{20}$. The value of $x$ is $......$.
$[ \text{Given} : h=6.63 \times 10^{-34} \, J \cdot s \text{ and } c=3.0 \times 10^{8} \, m \cdot s^{-1} ]$

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,$i.e.,$ $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$ and $C$ to $A$ respectively,which of the following statements is correct?

If the potential energy of an electron in the second orbit of $He^+$ is $-27.2 \, eV$,then calculate the double value of the energy of the first excited state of a hydrogen atom in $eV$.

According to Bohr's theory,
$E_{n} = \text{Total energy}, K_{n} = \text{Kinetic energy}, V_{n} = \text{Potential energy}, r_{n} = \text{Radius of } n^{\text{th}} \text{ orbit}$
Match the following:

Column $I$	Column $II$
$A$. $V_{n} / K_{n} = ?$	$P$. $0$
$B$. If radius of $n^{\text{th}}$ orbit $\propto E_{n}^{x}, x = ?$	$Q$. $-1$
$C$. Angular momentum in lowest orbital	$R$. $-2$
$D$. $1/r_{n} \propto Z^{y}, y = ?$	$S$. $1$